PSYCHOLOGY 820 Chapters Introduction Variables, Measurement, Scales Frequency Distributions and Visual Displays of Data

The Image of Statistics “Sadistic Statistics” How to feel about this course Descriptive Statistics Tabulating, depicting, and describing sets of data Inferential Statistics Generalizing from a sample to the entire population HI, I'M RALPH AND I HATE STATISTICS

Statistics and Mathematics Statistics is a branch of applied mathematics Intuition, logical reasoning, and simple arithmetic are the essential tools Similar to studying a language Extensive use of the computer (SPSS) A word to the wise (James 1:22) “Be ye doers of the word, and not hearers only, deceiving your own selves”.

Case Method The CHAPMAN data set is from a cholesterol study of 200 adults who were measured on several variables and followed for ten years. The HSB data set is from the High School and Beyond Study; achievement and demographic data are given for a national representative sample of 600 high school seniors. The EXERCISE data set contains data on certain exercise and smoking variables for a forty-person sample.

Variables and Their Measurement Variables are non-uniform characteristics (e.g., age) of observational units (e.g., persons). A measurement is an observation that is expressed as a number. Measurement involves assigning number to things according to rules. Measurements should be as precise and as valid as possible.

Measurement Scales Nominal Numerical naming is the most rudimentary form of measurement. Ordinal Achieved when a group of things can be ranked from low to high but has no information about the magnitude of the differences between the ranks. Interval The actual magnitude of the differences among the units is reflected in the numbers (equal differences in numbers correspond to equal differences in the amounts of the attribute measured). The zero point on the scale is arbitrary and does not represent an absence of the characteristic measured. Ratio Differs from interval measurement in that its zero point denotes the absence of the property measured.

Interrelationships Among Measurement Scales Level of measurement is not always straightforward The particular scale of measurement is influenced by the interpretation to be drawn from the data Exaggeration of the importance of the scale of measurement “On the statistical treatment of football numbers”

Continuous and Discrete Variables Continuous variables can take on any value within a certain range when measured such as weight, age, or reaction time. Discrete variables can take on only separated values when measured, such as number of children in a class or number of days absent.

Tabulating Data The search for order, organization, and lawfulness in our experience and observations leads to statistical summaries which can aid in the task of apprehending the relevant information in a complex data set.

Grouped Frequency Distributions To organize data into a grouped frequency distribution 1.Find the range (max-min) 2.Select the number of intervals (10-30) 3.Define the score limits for the intervals (each interval begins with a multiple of the class width) 4.Tally the observations into the intervals 5.Count the tallies within each interval and express as a frequency

Grouping and Loss of Information Some information is lost when the observations are grouped into intervals. Generally, the fewer the intervals, the greater the loss of information. The grouping that best reveals or portrays the important features of a distribution of scores for the intended audience is the main consideration.

Graphing a Frequency Distribution The three most common methods of graphing a distribution are the Histogram (bar graph) Frequency (or percentage) polygon Ogive curve (cumulative percentage)

Types of Distributions Bimodal Normal Negatively skewed Positively skewed Rectangular

Percentiles Percentiles are points in a distribution below which a given percent of the cases lie. Percentile norms are employed for assessing physical grown, performance on standardized tests, and many other purposes. Percentile scores allow comparison of relative performance on different variables. Percentiles or percentile ranks are very useful for descriptive purposes but have serious drawbacks when used in statistical inference.

Box-And-Whisker Plots The box-and-whisker plot (or box plot, for short) is a simple and useful graph for exploring and summarizing an array of data.

Stem-And-Leaf Displays Another method of portraying a set of data is the stem-and-leaf display which is simply a refined grouped frequency distribution.

Time-Series Graphs Standard statistical figure in business and economics Useful for identifying trends and changes in trends in ways that other representations of data cannot The X-axis (baseline) is time The vertical axis is a measure of the variable of interest Extrapolated projections into the future are shown by the dashed line.

Misleading Graphs: How To Lie With Statistics Distorted representation Misleading scaling and calibration Combination graphs